Existence results of totally real immersions and embeddings into $\mathbb {C}^N$
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- by Marko Slapar and Rafael Torres PDF
- Proc. Amer. Math. Soc. 146 (2018), 5463-5473 Request permission
Abstract:
We prove that the existence of totally real immersions of manifolds is a closed property under cut-and-paste constructions along submanifolds including connected sums. We study the existence of totally real embeddings for simply connected $5$-manifolds and orientable $6$-manifolds and determine the diffeomorphism and homotopy types. We show that the fundamental group is not an obstruction for the existence of a totally real embedding for high-dimensional manifolds in contrast with the situation in dimension four.References
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Additional Information
- Marko Slapar
- Affiliation: Faculty of Education, University of Ljubljana, Kardeljeva Pos̆c̆ad 16, 1000, Ljubljana, Slovenia – and – Institute of Mathematics, Physics and Mechanics, Jadranksa 19, 1000, Ljubljana, Slovenia
- MR Author ID: 740331
- Email: marko.slapar@pef.uni-lj.si
- Rafael Torres
- Affiliation: Scuola Internazionale Superiori di Studi Avanzati (SISSA), Via Bonomea 265, 34136, Trieste, Italy
- MR Author ID: 893311
- Email: rtorres@sissa.it
- Received by editor(s): December 22, 2017
- Received by editor(s) in revised form: March 22, 2018
- Published electronically: September 4, 2018
- Communicated by: Filippo Bracci
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 5463-5473
- MSC (2010): Primary 57R42, 32Q99
- DOI: https://doi.org/10.1090/proc/14234
- MathSciNet review: 3866882